Dominic Thiem saved three match points before beating Hubert Hurkacz for the first time to reach the semi-finals of the European Open on Friday.

Thiem was on the brink of being knocked out by the top seed in Antwerp, but fought back to win 3-6 7-6 (11-9) 7-6 (7-4).

The 2020 US Open champion fended off all three match points in a second-set tie-break to take a thrilling quarter-final the distance and then came out on top in another breaker to advance.

Thiem will do battle with Sebastian Korda for a place in the final after the American emphatically defeated eighth seed Yoshihito Nishioka 6-0 6-2.

Richard Gasquet moved into the last four at the expense of David Goffin and will face Felix Auger-Aliassime, who came from a set down to beat Dan Evans.

Matteo Berrettini remains in the hunt to win the Tennis Napoli Cup on home soil after a 6-2 6-3 quarter-final triumph over Taro Daniel.

Top seed Pablo Carreno Busta crashed out in Italy, losing 7-5 6-2 to Miomir Kecmanovic, who will face Lorenzo Musetti after he got the better of Daniel Elahi Galan. Mackenzie McDonald will come up against Berrettini after getting past Zhang Zhizhen.

Stefanos Tsitsipas sealed a Stockholm Open semi-final spot with a 7-5 6-3 win over Mikael Ymer and will take on Emil Ruusuvuori, who eliminated Frances Tiafoe.

Holger Rune and Alex de Minaur meet in the other last-four match in the Swedish capital following wins over Cameron Norrie and Denis Shapovalov respectively.

J.J. Wolf was no match for Felix Auger-Aliassime in the final of the Firenze Open, as the Canadian won 6-4 6-4 in Florence.

Auger-Aliassime is targeting a place in the end-of-season ATP Finals and took a huge step towards securing such a spot on Sunday.

The top-seeded 22-year-old only dropped one set throughout the tournament and has now won his second ATP Tour-level title.

His victory over Wolf, the world number 75 who will rise to 56 on Monday, took only one hour and 41 minutes.

"It never gets old. Winning, it always feels like the first time," Auger-Aliassime, the new world number 10, said in his on-court interview.

"It's so special to win, especially here. I had a fantastic week and it's been amazing.

"Every final is tough, it's the two best players of the week. Of course you try to win more than you lose the finals, and that's why I came out here today ready to give everything.

"We had some very tough rallies in the second set, feeling tough physically. But you keep pushing, try to keep the level high.

"But there's no magic. Sometimes you win, sometimes you lose, but of course I'm really happy because I came here [as] the first seed.

"I was the favourite in all of my matches on paper. It's never an easy position, so to come out and win my four matches with confidence and conviction, it's really good for my confidence."

Wolf saved nine of the 12 break points he offered yet could not make any inroads against Auger-Aliassime's serve, with the champion winning without conceding on his service game.

Andrey Rublev set up a final meeting with Sebastian Korda at the Gijon Open, overcoming Dominic Thiem in straight sets in the last four.

The world number nine battled through an up-and-down opener before remaining patient to seal the second set and the match on Thiem's serve, taking a 6-4 6-4 victory.

Russian Rublev has now won eight successive sets of tennis against the 2020 US Open champion, and he is one win away from his fourth title of 2022 after triumphs in Belgrade, Dubai and Marseille.

Speaking on court after the win, Rublev said: "I was lucky I played a really good game and Dominic helped me out a little bit.

"Then I felt more confident and I was able to win in two sets, which was the most important thing. This week I have been playing really well, and I'll try to show my best tennis of the week tomorrow."

Korda will be Rublev's opponent on Sunday after the American saw off France's Arthur Rinderknech for a 7-6 (7-2) 6-3 win.

Meanwhile, at the Firenze Open, top seed Felix Auger-Aliassime saw off home favourite Lorenzo Musetti 6-2 6-3, moving one step closer to a second ATP Tour title.

The Canadian will face JJ Wolf in the final in Florence, after the American clinched a 6-4 6-4 win over Sweden's Mikael Ymer.

Andy Murray's run at the Gijon Open came to an end with a three-set loss to Sebastian Korda on Friday, dashing his hopes of a semi-final appearance in Spain.

Murray earned his fourth Tour-level quarter-final spot of 2022 by beating Pedro Cachin, but American Korda defeated the former world number one 6-4 1-6 6-1.

Korda will face Arthur Rinderknech in the last four after he upset second seed Pablo Carreno Busta, taking an epic final-set tie-break to triumph 4-6 6-3 7-6 (18-16).

The other side of the draw will play host to an enticing semi-final meeting between Dominic Thiem and top seed Andrey Rublev after they secured straight-sets wins over Francisco Cerundolo and Tommy Paul respectively.

Thiem said after his 6-4 6-3 triumph over Cerundolo: "From the first match on, I have felt great on this court.

"It is very important for me as I am trying to climb up the rankings. The semi-finals at an ATP event is helping a lot."

Meanwhile, top seed Felix Auger-Aliassime beat Brandon Nakashima 6-3 6-4 to reach the Firenze Open semi-finals, where he will face home favourite Lorenzo Musetti.

The third seed from Italy downed Mackenzie McDonald 6-3 6-2, but fellow seed Alexander Bublik went down 3-6 7-5 6-1 to J. J. Wolf.

Andy Murray overturned a first-set deficit to defeat Pedro Cachin gripping 2-6 7-5 7-6 (7-3) and book his spot in the quarter-finals of the Gijon Open.

The three-time grand slam champion lost a 56-minute opening set but showing his trademark doggedness to defeat his Argentine opponent and earn a fourth Tour-level last-eight berth of the season.

It sets the Briton up with a last-eight encounter against Sebastian Korda after the unseeded American delivered the upset of the day to knock out third seed and home favourite Roberto Bautista Agut in a 5-7 6-4 6-4 triumph.

Elsewhere, first seed Andrey Rublev saw off a fightback from Ilya Ivashka to also book his place in the quarter-finals, with his reward a tie against Tommy Paul.

At the Firenze Open, top seed Felix Auger-Aliassime saw off a second set scare from Germany's Oscar Otte, with the Canadian ultimately triumphing 6-4 6-7 (2-7) 6-2.

He will meet eighth seed Brandon Nakashima, who ran out comfortably in straight sets against Altug Celikbilek with a 6-3 6-4 win.

Third seed Lorenzo Musetti also made smooth work on his own turf, with a 6-3 6-0 demolition job against Bernabe Zapata Miralles, to set up an encounter in the last eight with Mackenzie McDonald.

World number nine Andrey Rublev comfortably beat qualifier Laslo Djere 6-4 6-3 to secure his place in the second round of the Astana Open.

The fifth seed found a crucial break of serve when leading the opener 5-4 to take the first set in Kazakhstan, before winning the next three games to put himself in the ascendancy in the second.

And despite a desperate last stand to stay in the match from Djere, Rublev held serve three times with relative ease to finish off his Serbian opponent.

Eighth seed Felix Auger-Aliassime served 14 aces to Roberto Bautista-Agut's two in their first-round match, but it was the Spaniard who advanced with a 6-4 7-6 (8-6) success.

Meanwhile, world number 10 Hubert Hurkacz overcame Francisco Cerundolo in straight sets.

Adrian Mannarino, the runner-up in Astana in 2020, came from a set down to beat Stan Wawrinka – playing as a wildcard – 1-6 6-2 6-3, and qualifier Zhizhen Zhang romped to victory with a superb third set to seal a 4-6 6-4 6-1 comeback win of his own over Aslan Karatsev.

At the Tokyo Open, fourth seed Frances Tiafoe cruised into the second round with a 6-3 6-4 triumph over Yasutaka Uchiyama, one of three Japanese players who crashed out at the first-round stage of their home tournament.

Uchiyama's countrymen Taro Daniel and Shintaro Mochizuki also tasted defeat at the hands of Bernabe Zapata Miralles and Brandon Nakashima, respectively.

Roger Federer said he felt the pain of Team Europe's first Laver Cup defeat as the World team crashed the Swiss great's farewell party in breathtaking style.

The final event of Federer's playing career veered off the script as he and Rafael Nadal lost in doubles on Friday, before the team collectively succumbed to a 13-8 defeat in London.

Stunning singles wins for Felix Auger-Aliassime and Frances Tiafoe on Sunday, against Novak Djokovic and Stefanos Tsitsipas respectively, followed a doubles thriller that saw Auger-Aliassime and Jack Sock topple Andy Murray and Matteo Berrettini.

After Team Europe won the first four editions of the Laver Cup, this time they had to swallow the bitter pill of defeat, with Federer sorry to sign off on a losing note.

"Of course I'm disappointed," he said. "I was on the team. I almost lost my voice. My hands hurt from clapping.

"So, yes, I am disappointed. We wish the result would be different. I told Andy [Murray] in the locker room, I don't like losing. It's not fun. It just leaves not the best taste, you know. I think once you have been there and taste success, it's just not the same."

He said his goodbye tournament had been a mix of highs and lows.

"This weekend has been all over the place for me," said the 41-year-old Swiss. "I enjoyed it, but it's unfortunate that we couldn't get the win tonight."

Federer denied he has his eyes set on becoming the next Team Europe captain. Incumbent skipper Bjorn Borg and Team World counterpart John McEnroe have indicated next year's match could be the last that they helm, which would create an appealing vacancy.

"No plans there. Bjorn's doing a great job," said Federer. "Who knows, maybe one day, but we don't have any plans so far."

Next year's match takes place in Vancouver, and Federer will certainly have a role of some sort to play, given he is a co-founder of the event.

"I went through all different types of Laver Cups so far: the first one, the winning teams, now this time on the losing team," Federer said. "There was also one where I was hurt last year but seeing it more from the stands and from the fans' perspective, and now deep on the inside with retirement.

"I have enjoyed the Laver Cup in many different ways, and next year again will be totally different. I'm looking forward to it, and I'm sure Vancouver is going to be fantastic."

Asked what he would miss about tennis, Federer said: "Not the losing press conferences, I tell you that. They are the worst."

Felix Auger-Aliassime and Frances Tiafoe played starring roles as Team World won three matches on the spin on Sunday to claim a first Laver Cup triumph over Team Europe.

Team World went into the final day of action at the O2 Arena in London sitting four points behind their opponents, but they produced a stirring fightback to claim the trophy at the fifth time of asking.

Central to their success was Canadian Auger-Aliassime, who beat Novak Djokovic in singles after successfully teaming up with Jack Sock in the doubles.

Holding an 8-4 lead from Saturday, many expected Team Europe to breeze it from there, but John McEnroe's World team had other ideas and earned a 13-8 victory. 

Up first in the doubles were Auger-Aliassime and Sock, who lost the first set to Team Europe's Andy Murray and Matteo Berrettini.

However, the World duo roared back to deliver three points for their team by claiming a 2-6 6-3 10-8 victory.

Djokovic won two matches for Team Europe on Saturday, yet he was powerless to stop Auger-Aliassime in their singles clash. The 22-year-old Canadian landed a 6-3 7-6 (7-3) over the Wimbledon champion.

That moved Team World 10-8 ahead in the overall contest, setting the stage for a decisive clash between Stefanos Tsitsipas and Frances Tiafoe, with a further three points at stake.

Greek Tsitsipas won the first set, but 24-year-old American Tiafoe stormed back to win an epic tie-break in the second on his way to a 1-6 7-6 (13-11) 10-8 success.

Novak Djokovic played a vital role in Team Europe opening up a four-point lead in the Laver Cup as he won in singles and doubles upon his return to the ATP Tour after a three-month absence.

Djokovic had not played since taking his grand slam count to 21 with the Wimbledon title in July, but he looked as if he had hardly been away as the Serbian beat Frances Tiafoe and then teamed up with Matteo Berrettini in the doubles.

Tiafoe beat Rafael Nadal at the US Open earlier this month and combined with Jack Sock on Friday to defeat the Spaniard again in what was Roger Federer's last ever match, but the American could not get to grips with Djokovic in Saturday's final singles contest.

Djokovic's 6-1 6-3 win secured two points for Team Europe to put them out in front, and he was involved again in the last of the day's action as the team's advantage doubled to four points.

Berrettini and Djokovic tussled with Sock and Alex de Minaur and ultimately had too much, winning 7-5 6-2 in less than an hour and a half.

Earlier, Taylor Fritz's three-set triumph over Cameron Norrie put Team World briefly back on level terms.

Fritz made a brutal start but ended up being forced to a match tie-break, eventually coming through with a 6-1 4-6 10-8 victory.

That wiped out the two-point lead Berrettini had given Europe in the first match of the day, with the Italian edging Saturday's most gruelling tussle.

He saw off Felix Auger-Aliassime 7-6 (13-11) 4-6 10-7, and despite finding himself on court for over two hours, Berrettini was still sharp enough to emerge victorious alongside Djokovic.

Carlos Alcaraz fell to a defeat to fellow youngster Felix Auger-Aliassime in his first match as world number one.

Alcaraz triumphed at the US Open on Sunday, beating Casper Ruud to clinch his first grand slam title and, in the process, become the youngest world number one since the rankings were first published in 1973.

The 19-year-old is the second-youngest male player to win the title at Flushing Meadows in the Open Era, and only the third player since the majors welcomed professionals in 1968 to win the US Open title at his first or second main draw appearance after Arthur Ashe and Rod Laver (in the first two editions of the tournament).

Yet back on home soil in Spain on Friday, Alcaraz was unable to claim victory in his first match since becoming number one, as he went down 6-7 (3-7) 6-4 6-2 to Auger-Aliassime in the Davis Cup Finals.

Canada's Auger-Aliassime did not concede a break point as he dragged his country level in their tie with Spain in Valencia, teeing up a doubles decider after Roberto Bautista Agut defeated Vasek Pospisil 3-6 6-3 6-3.

Auger-Aliassime, 22, has won both of his career matches against Alcaraz, after defeating him in the US Open quarter-finals last year.

Britain's Jack Draper claimed one of the biggest scalps of the US Open so far after stunning sixth seed Felix Auger-Aliassime in a 6-4 6-4 6-4 victory to progress to the third round.

The 20-year-old defeated last year's Flushing Meadows semi-finalist to reach the last 32 in his first main-draw appearance at the final major of the season.

On the back of a second-round appearance at Wimbledon earlier this year, it represents Draper's best showing at a Grand Slam to date – and at few points did the Briton look at risk of letting the tie slip away from his grasp.

Draper saved all three of the break points he faced and took three of the 10 presented to him in a fine showing at Louis Armstrong Stadium.

For the Canadian, it brings a premature end to what the 22-year-old likely hoped would be a promising tournament that could have seen him go one better than last year.

He is the third top-10 seeded men's player to be eliminated, following first-round exits for Stefanos Tsitsipas and Taylor Fritz against qualifiers Daniel Elahi Galan and Brandon Holt respectively.

Nick Kyrgios' red-hot form has been halted after going down in three sets to eighth seed Hubert Hurkacz in the quarter-finals of the Canadian Open on Friday.

Hurkacz ran away with victory, triumphing 7-6 (7-4) 6-7 (5-7) 6-1 in one hour and 46 minutes in Montreal.

Wimbledon finalist Kyrgios had come into the encounter fresh from winning 15 of his past 16 matches, including lifting the title at last week's Washington Open. Kyrgios' run had fueled expectations around him at the upcoming US Open.

"Nick has been playing some incredible tennis throughout the past weeks, so it is a pleasure playing against him," Hurkacz said post-match in his on-court interview.

"I started really well. Nick was maybe a little bit injured, which might have hurt his serve. With both of us serving so well, that few per cent can make the difference."

Kyrgios was quick on serve but the 25-year-old Pole eventually ground him down, prevailing in the third set aided by an early break.

That break came after Kyrgios gave up two double faults, leading to the Australian to complain to the umpire about his opponent's mid-match break for a change of clothes.

The Australian was unable to break Hurkacz's serve throughout the match, with the Pole edging the aces count 20-19, while he was also superior on return. Kyrgios had more winners (55-47), but more unforced errors (24-13).

Hurkacz, who will face fourth seed Casper Ruud in the semi-finals, is the only former Masters 1000 champion left in the draw.

Ruud cruised into the last four with a 6-1 6-2 victory over hometown hero Felix Auger-Aliassime who was brushed aside in one hour and 14 minutes.

The Norwegian's win marks his third ATP Masters 1000 semi-final of the season, with the Canadian plagued by 21 unforced errors compared to Ruud's eight.

Unseeded Briton Daniel Evans fought back from a lopsided opening set to knock off Tommy Paul 1-6 6-3 6-4.

Evans will face Spaniard Pablo Carreno Busta after he defeated Jack Draper 7-6 (7-4) 6-1 in just under two hours.

Australia's Nick Kyrgios has now won 15 of his past 16 matches after defeating compatriot Alex de Minaur 6-2 6-3 in the third round of the Canadian Open – with his only loss coming in the Wimbledon final against Novak Djokovic.

Fresh off his first singles title since 2019 when he won last week's Washington Open, Kyrgios collected his ninth consecutive victory in impressive fashion, showing no difficulty in navigating his first-ever matchup against his fellow countryman.

He won the first four games of the match, and snatched a break in the first game of the second set to book his quarter-final against Poland's Hubert Hurkacz.

Hurkacz, the eighth seed, had to come back from a set down to defeat Spain's Albert Ramos-Vinolas 6-7 (6-8) 6-2 7-6 (7-3). He struggled with his serve early, with four double faults in the opening frame, but cleaned it up as the match went on, double-faulting only once in the last two sets.

England's top hope Cameron Norrie suffered a disappointing 6-3 6-4 defeat at the hands of world number nine Felix Auger-Aliassime, but Daniel Evans and Jack Draper made it through to fly the flag.

Evans pulled off an upset win to beat 10th seed Taylor Fritz 7-6 (7-5) 1-6 7-5, and 20-year-old Draper was up a set when 17th seed Gael Monfils retired with an injury at 6-2 0-2.

American Tommy Paul claimed another scalp with his 6-4 6-2 victory against 13th seed Marin Cilic, giving him back-to-back wins against top-15 opponents after emerging triumphant against Carlos Alcaraz in the previous round.

In the final match of the day, Pablo Carreno-Busta beat his third top-30 opponent of the week with a 6-2 6-4 result against Italy's Jannik Sinner, following strong successes against Matteo Berrettini and Holger Rune.

Nick Kyrgios started his Friday by finishing off his third-round win against Reilly Opelka, and his business was not finished until after 1am local time when he defeated Frances Tiafoe 6-7 (5-7) 7-6 (14-12) 6-2 in the quarter-final.

Due to length rain delays on Thursday, Kyrgios was one of five players forced to abandon their matches and return to finish them first thing on Friday, with Kyrgios and Russia's Andrey Rublev the only two to successfully navigate both.

Tiafoe defeated Botic van de Zandschulp 4-6 6-2 6-3 in the morning, but Kyrgios' ability to keep his service games short was a decisive factor, winning the ace count 35-14 and not conceding a single break all match.

Rublev had to deal with Maxime Cressy in the morning, winning 6-4 7-6 (10-8), setting up a quarter-final later at night against J.J. Wolf after the American defeated Holger Rune 7-5 4-6 6-3.

Rublev made his second match look far easier, cruising through 6-2 6-3 to earn a semi-final against Japan's Yoshihito Nishioka after he needed over three-and-a-half hours to beat Daniel Evans 7-6 (7-5) 4-6 7-5.

In an all-unseeded semi-final, Kyrgios will play Sweden's Mikael Ymer, who fought his way past Sebastian Korda 6-2 5-7 6-3 after the American beat Bulgaria's Grigor Dimitrov 4-6 6-1 6-2 earlier in the day.

Meanwhile, down in Mexico at the Los Cabos Open, Daniil Medvedev earned his spot in the final by defeating Serbia's Miomir Kecmanovic 7-6 (7-0) 6-1.

Medvedev will play England's Cameron Norrie for the title after he prevailed in arguably the match of the tournament against top-10 talent Felix Auger-Aliassime 6-4 3-6 6-3.